9. Almudena Cathedral / Catedral de la Almudena
8. Puerta Del Sol
7. Temple of Debod / Templo de Debod
6. Rastro Market / El Rastro
5. Retiro Park / Parque de Retiro
4. Reina Sofia Museum / Museo Reina Sofia
3. Plaza Mayor
2. Royal Palace / Palacio Real
1. Prado Museum / Museo del Prado
The Madrid Ruta/Route 1 passes by all of the above places. The tour starts at Paseo del Prado (boulevards) where the Prado Museum (1) is closely located, passes by Plaza de Cibeles (10), Temple de Debod (7), Royal Palace (2) and Almudena Cathedral (9) which is next to the palace. Then proceed to Rastro Market (6) along Calle Toledo which is a market that open only on Sundays and public holidays. Thereafter followed by Plaza Mayor (3), Puerta del Sol (8), Reina Sofia Museum (4) and ends at Real Jardin Botanico. The Retiro Park (5) is just beyond the garden.
Alternatively there's Madrid to the river tours from Plaza Mayor which are walking tour that you can take on your own. A map on the routes can be obtained from the info centre in Plaza Mayor.